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CGI Math Should Be A Party

As always, I hope you are happy, healthy, and loved.

This has nothing to do with math, but I had a huge ‘aha’ the other day. I have been putting on shoes that I know are too tight and blaming the show when my foot hurts.

Have you ever had a
relationship with a friend, family member, or coworker that was not working out despite your best efforts?
The relationship was/is filled with constant miscommunications, misunderstandings, hurt feelings, and passive aggressiveness. Spending time with this person or people is sometimes amazing and often not.

I have decided that if someone(s) leaves me feeling emotionally drained, unhappy, bitter, or confused, I am limiting or eliminating that relationship. No more forcing things to work.
I will no longer put on the wrong size shoe and blame the shoe when my foot hurts. Now I know it’s just not a good fit.

I hope you have a wonderful week.
I hope all of your shoes fit you well.

Book of the Week

ELA

Use sensory details to describe a person, place, or thing.

How do the parents feel when they see the watercress on the side of the road? How do the parent’s feelings differ from the children’s? Why might they feel differently?

Identify and list words with -ing endings.

Math 

Compare the cost of a bag of vegetable seeds to a pound of vegetables bought in the store.
Calculate the number of calories in a bag of french fries compared to the calories in a bag of watercress.
If the family gathered 4 bags of watercress from the roadside and ate 1/3 of a bag a night, how long would the watercress last?

Force vs. Flow

Think of Cognitively Guided Instruction in Math (CGI) like a party. Ideally, you would prepare your materials (food, drinks, plates, and cups), invite a diverse group of guests, create a positive environment, and create moments that encourage your guests to mix and mingle, e.g., music, games, maybe a piñata (I love a piñata at an adult party).

Your role at the party would be to greet guests, direct them toward the food, drinks, and bathroom, and introduce new people to one another. Occasionally, you might pause the festivities to tell the guests dinner is served or the piñata is ready to be hit, but your number one job is to mix and mingle.

The above creates a festive atmosphere where people can make new friends, fall in love, build connections, and enjoy life. Your most important job is mixing, mingling, and keeping the party flowing.
This is also the best recipe for a successful CGI math lesson.

What often happens in classrooms where CGI is being implemented is that the party proceedings are forced rather than flowing. The hosts may not have prepared all the required materials, e.g., math tools and manipulatives appropriate for the grade level or lesson (number charts, coins, base ten blocks). So, the guests (students) need help to complete or get started on the task. Imagine a tray of food with no serving spoon. Your guests must track you down, ask for the spoon, and stop you from mingling because they don’t have the tools they need to help themselves.

Like a great CGI teacher, a good host creates the environment, provides the appropriate materials, and invites students to different foods or activities but never forces them to do something that makes them uncomfortable.

What do your mathematicians look and act like when doing math?

Are they asking their host for everything along the way, or can they move through the problems independently and easily?
Is the set party/math lesson set up so guests can be independent, or do they need you to survive?

Can the guests talk to whomever they want or only talk and listen to you?

Is the party flowing?

Panic at the disco.

A strong CGI teacher paces out their instruction by planning backward and allotting enough time for each stage of the party. Proper planning prevents panic. Proper planning allows students to dive deeply into mathematics and connect conceptual and procedural knowledge with ample time for procedural fluency.

A strong CGI teacher thinks about their instructional time for a whole year, unit, and day.

If there are 180 days of school a year, subtract approximately
-12 days for performances, field trips, professional development, etc.
– 30 days of testing (state, district, units)
That leaves teachers with approximately 138 instructional days.

If there are approximately six major content areas (addition, subtraction, multiplication, division, fractions, and decimals), it leaves approximately 23 days of instruction per content area (not including testing days).

Now with those 23 days of instruction per unit, are we forcing or flowing? How are the 23 days of instruction mapped out?

Professional Development Opportunities

If you want insight into Cognitively Guided Instruction, my Grassroots Workshop is an excellent place to begin.

If you want in-person support at your school site, email Danielle@TeachingOneMoore.org. I am currently booking dates for the 2023- 2024 school year. I would love to meet you.

Are you the performer or the producer?

What does day one look like when envisioning your twenty-three days of instruction? What should students be able to do on the first day of a unit, the ninth day, and the twenty-third day? What is your role, and what is your students’ role? How do these roles shift throughout each unit?

In many classrooms I visit (especially those not implementing CGI), day one often looks very similar to day nine and day twenty-three. The teacher is the lead actor, producer, and director.

Scenario 1: The teacher stands in front of the class, explains the content or standard being taught, gives examples of the procedure to use that day, and has the students practice with feedback and redirection from the teacher.
The same routine is repeated on day two with the same or a new procedure as the focus. The teacher may pull a small group and repeat the steps for the procedure.

Day twenty-three looks much like days one and two. Procedures are reviewed, and the teacher explains how to perform the steps. The teacher provides feedback, and the students implement the feedback.

Scenario 2: The teacher presents a word problem for students to solve. The teacher unpacks or reads the problem to or with the class. The students then work on the problem in a small group or independently. The teacher mixes and mingles with different students, perhaps lingering with one or two students a little longer than the others. The teacher then ends the lesson by asking a couple of students with the most interesting strategies to explain how they solved the problem to the class.

On day two, the teacher may begin the lesson by reflecting on a student’s strategy from the day before. The teacher might suggest different students with different approaches collaborate; the teacher might coach students to try new tools or techniques to get the best performance out of them.

Day twenty-three looks much like days one and two. The teacher poses a word problem and unpacks it with the students, and students solve the problem using any strategy they are comfortable with, usually resulting in a correct answer.

Scenario 3: What could be revised in both of the above scenarios?

A good party has a balance.

Scenario 3:
The teachers’ and students’ roles and responsibilities shift over a day, a unit, and a year.

Day One: Pose real-world problems that are relatable to students. Unpack the problem with students. Students are given opportunities to make sense of word problems with hands-on manipulatives, drawings, or equations. Time is made for two to three students to share their self-generated strategies.

The process looks very similar on day two, except two to three students share their strategies. Notice how a second day of engagement with the problem type and exposure to the thinking of others allows increases understanding, accuracy, and excitement.

Day 3:  the teacher asks SOME students what equations, expressions, or models represent the problem. The teacher pulls small groups and focuses on refining behaviors, e.g., organization and counting accuracy and efficiency.

Day 9: Students in the upper grades read the problems themselves. The students are making more efficient drawings and using them to record efficient equations and expressions. Various students are using multiple representations to solve and verify their work. They are linking concepts to procedures naturally and with ease. They are embedding measurement and data standards into their daily work.

On day 15: Students create and pose real-world problems to the class to solve because they understand the concept and procedures so well. (FYI- a group of kindergarteners became the authors of their math problems today.) Students in grade one learn to write explanations about how they solved the problem and justify their answers.

By day twenty: the students can comfortably look at a page of equations or expressions and pull from experiences and the previous nineteen days to solve the problems. They can look at the numbers and symbols and create stories to help them solve them. They can envision or draw the tools to make sense of the values and relationships. They can create a ratio table or number line to efficiently organize and solve the information.

They can collaborate with a helpful partner to confirm their findings. They can ask open-ended questions to coach someone stuck, e.g., “What strategy will help you solve this problem easier, a ratio table, number line, or base ten blocks?”

On day twenty-four: students take a test that mirrors much of what they have been doing the past 23 days.

The roles and responsibilities between teacher and student shift over a day, unit, and year with students slowly taking on more responsibilities. Students can play an active role in the learning community. They learn how to solve problems, who best to collaborate with, how to advocate for themselves, and how to ask good, inspired questions.

Do you go hard at the beginning or do you ease your way in?

Some people approach parties differently. Some go hard right from the beginning, drinking, and eating, and burn out fast. Others ease their way and can maintain all night.

What approach do you take to mathematics instruction?

Do students practice challenging problems with challenging numbers for twenty-three days with your guidance because you want to prepare them for a test? (Burnout and codependence are likely for many).

Do you give students simple problems they can relate to with simple numbers they can use for twenty-three days and then expose them to challenging test-like problems on days twenty through twenty-three?

Do you turn up the heat slowly and give students simple problems they can relate to with simple numbers at the beginning, give them slightly more challenging problems with more challenging numbers and less teacher support in the middle, and end with very challenging problems and numbers that are similar to the test with little to no teacher support?

Students become dependent on teacher-taught procedures when we pose challenging problems with challenging numbers on day one. Students become independent problem-solvers when we introduce simple problems with simple numbers and up the rigor over time.

Everyone needs a good party trick.

Trick 1:
Thoughtfully plan out your instruction to increase rigor and prepare students for assessments by day twenty-three.
Trick 2:
Make sure your students know the real meaning behind mathematical symbols. What does 1/2 x 1/3 look like in real life?
Trick 3:
Be kind and consider the needs of all of your guests. Don’t leave someone sitting in the corner or let others get too drunk with power.
Trick 4:
Set up your party so guests have access to everything they need and you can be free to mix and mingle, e.g., confer and work with small groups.

 
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